Identify the type of surface represented by the given equation.
-$$\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 7 } + \frac { z ^ { 2 } } { 6 } = 1$$
A) Ellipsoid
B) Paraboloid
C) Sphere
D) Elliptical cone

Question

Quizplus · Accepted Answer

The given equation represents an ellipsoid because the coefficients of $x^2$, $y^2$, and $z^2$ are different and have the same signs. Also, since the constant on the right side is positive, it indicates that the surface is bounded, i.e. the ellipsoid.

Identify the Type of Surface Represented by the Given Equation x22+y27+z26=1\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 7 } + \frac { z ^ { 2 } } { 6 } = 12x2​+7y2​+6z2​=1

Identify the Type of Surface Represented by the Given Equation $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 7 } + \frac { z ^ { 2 } } { 6 } = 1$